Question

a right - circular cylinder has a radius of 6 inches and a height of 5 inches. decrease the height and radius by 10%. use the formulas (v=pi r^{2}h) and (sa = 2pi rh+2pi r^{2}) to answer parts a through b below.
a. find the volume v and surface area sa of the original cylinder.
the volume is (v=) 565.49 cubic inches.
(round to the nearest hundredth as needed.)
the surface area is (sa=) 414.69 square inches.
(round to the nearest hundredth as needed.)
b. find the volume v and surface area sa of the new cylinder.
the volume is (v=square)

Explanation:

Step1: Calculate new radius and height

The original radius $r = 6$ inches and original height $h=5$ inches. Decreasing by 10% means new radius $r_{new}=r\times(1 - 0.1)=6\times0.9 = 5.4$ inches and new height $h_{new}=h\times(1 - 0.1)=5\times0.9 = 4.5$ inches.

Step2: Calculate volume of new cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$. Substitute $r_{new}=5.4$ inches and $h_{new}=4.5$ inches into the formula: $V=\pi\times(5.4)^{2}\times4.5=\pi\times29.16\times4.5\approx410.31$ cubic - inches.

Answer:

$410.31$